\documentclass[student]{LSRslides}

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\usepackage{movie15}
\usepackage[english]{babel}

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\title{Online Segmentation of Haptic and Motion Time Series Data}
\presenter{Julian Bernhard}
\presentermail{julian.bernhard@mytum.de}
\addauthor{S. Hirche}
\addauthormail{hirche@tum.de}
\supervisor{Prof. Dongheui Lee \& Dipl.-Ing. Jose Ramon Medina Hernandez}
\typeofpres{Bachelor Thesis}

\usepackage{pstricks}
\usepackage{bm}
\usepackage{pifont}
\usepackage[scriptsize]{subfigure}
\usepackage{shadow}
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\setlength{\unitlength}{\textwidth}

\def\Tiny{ \font\Tinyfont = cmr10 at 10pt \relax  \Tinyfont}

\begin{document}

\begin{frame}
   \titlepage
\end{frame}

% \begin{frame}
%     \frametitle{Overview}
%      \tableofcontents[hideallsubsections, pausesections]
% \end{frame}

\section{Introduction}

\begin{frame}
 \frametitle{Motivation}
\begin{pspicture}(1.0\textwidth,-5)(0,3) %\psgrid  
  \rput[tr](4,-0.5){\frame{\includegraphics[width=4cm]{./Bilder/Bilder/humanrobot_5.eps}}}
  \rput[tm](8,-1){\frame{\includegraphics[width=2.5cm]{./Bilder/Bilder/humanrobot_3.eps}}}
    \rput[tm](5.5,0.2){\frame{\includegraphics[width=3.5cm]{./Bilder/Bilder/humanrobot_1.eps}}}
     \rput[br](4,-0.4){\frame{\includegraphics[width=2.5cm]{./Bilder/Bilder/humanrobot_4.eps}}}
    \rput[lb](6.8,-0.6){\frame{\includegraphics[width=1.5cm]{./Bilder/Bilder/humanrobot_2.eps}}}
    
  \rput[tm](5.5,2.8){\parbox{\textwidth}{
    \begin{block}{Goal}
	\centering Enabling autonomous robots to learn motion primitives from observed behavior during interaction with humans
    \end{block}}}
%   \rput[tl](0,-3.2){\parbox{3.5cm}{\scalebox{0.5}{\Tiny Picture sources:\\ \begin{tabular}{rl}
%                                                              -& http://www.euron.org/ \\
% 								   -& http://www.cotesys.de/\\
% 								   -& http://images.sciencedaily.com/\\
% 								   -& http://dasl.mem.drexel.edu/\\ 
% 								   -& http://cyphynets.lums.edu.pk/\\
%                                                             \end{tabular}}}}

   
\end{pspicture}
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%Source pictures
%http://www.euron.org/
%http://www.cotesys.de/
%http://images.sciencedaily.com/
%http://dasl.mem.drexel.edu/
%http://cyphynets.lums.edu.pk/+
\begin{frame}
	\frametitle{Primitive Base Learning}		   
	\begin{figure}
	 
	    \begin{pspicture}(1.0\textwidth,0.4\textwidth)
	     % \newrgbcolor{back}{0.8 0.8 1.0}
              %\put(0.09,-0.07){\psframe[linecolor=black,
		%		fillcolor=back,
		%		fillstyle=solid]
		%		(0.7,2.1)(6.7,4.53)
		%		  }
	       \put(0.9,-0.42){ \psfrag{da}[c][c]{\parbox{3cm}{\footnotesize \centering continuous \\haptic and motion time series}}
	  \psfrag{se}[c][c]{\parbox{3cm}{\footnotesize \centering online segmentation}}
	  \psfrag{en}[c][c]{\parbox{3cm}{\footnotesize \centering HMM encoding}}
	  \psfrag{tr}[c][c]{\parbox{3cm}{\footnotesize \centering primitive \\knowledge base}}
	 \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/clustering_base.eps}}
             \end{pspicture}
          	   \caption{Schematic overview of a possible learning procedure for motion and haptic data }
         \end{figure}
\end{frame}


\begin{frame}
	\frametitle{Online Segmentation}
	% State of the Art	   
	\only<1>{\begin{figure}
	 
	    \begin{pspicture}(1.0\textwidth,0.282\textwidth)
	      \newrgbcolor{back}{0.95 0.95 1.0}
              \put(0.09,-0.07){\psframe[linecolor=black,
				fillcolor=back,
				fillstyle=solid]
				(0.7,2.1)(6.7,4.58)
				  }
	       \put(0.9,-0.4){ \psfrag{da}[c][c]{\parbox{3cm}{\footnotesize \centering continuous \\haptic and motion time series}}
	  \psfrag{se}[c][c]{\parbox{3cm}{\footnotesize \centering online segmentation}}
	  \psfrag{en}[c][c]{}
	  \psfrag{tr}[c][c]{}
	  \psfrag{desc}[t][c][1.1]{\parbox{5cm}{\tiny State of the Art: \begin{itemize}
	                                                           \item Mixture of Experts \cite{Mueller95analysisof},\cite{Pawelzik96annealedcompetition}
								   \item Statistical Model\\ of Low-Level actions \cite{DefLowLev}
								  \item  Angular Velocity Based Methods \cite{eval_metrics}
	                                                          \end{itemize}}}
	 \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/clustering_base_segmarked.eps}}
             \end{pspicture}
         \end{figure}
        }

	% HMM Based Approach
	 \only<2>{\begin{figure}
	 
	    \begin{pspicture}(1.0\textwidth,0.282\textwidth)
	      \newrgbcolor{back}{0.95 0.95 1.0}
              \put(0.09,-0.07){\psframe[linecolor=black,
				fillcolor=back,
				fillstyle=solid]
				(0.7,2.1)(6.7,4.58)
				  }
	        \put(0.09,-0.07){\psframe[linecolor=black,
				fillcolor=back,
				fillstyle=solid]
				(-1,-1.2)(5.0,-0.4)
				  }
	       \put(0.9,-0.4){ \psfrag{da}[c][c]{\parbox{3cm}{\footnotesize \centering continuous \\haptic and motion time series}}
	  \psfrag{se}[c][c]{\parbox{3cm}{\footnotesize \centering online segmentation}}
	  \psfrag{en}[c][c]{}
	  \psfrag{tr}[c][c]{}
	  \psfrag{desc}[t][c][1.1]{\parbox{5cm}{\tiny State of the Art: \begin{itemize}
	                                                           \item Mixture of Experts \cite{Mueller95analysisof},\cite{Pawelzik96annealedcompetition}
								   \item Statistical Model\\ of Low-Level actions \cite{DefLowLev}
								  \item  Angular Velocity Based Methods \cite{eval_metrics}
	                                                          \item  \footnotesize A HMM based approach \cite{DynHMM} 
                                                  \end{itemize}}}
	 \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/clustering_base_segmarked.eps}}
             \end{pspicture}
         \end{figure}}


\end{frame}

\begin{frame}
    \frametitle{An HMM Based Segmentation Approach\cite{DynHMM}}
      \centering
 \only<4-5>{\begin{figure}
             \psfrag{s1}[c][c]{\(s_1\)}
	      \psfrag{s2}[c][c]{\(s_2\)}
	      \psfrag{sT}[c][c]{\(s_T\)}
	      \psfrag{x}[c][l]{\(\vec{x}\)}
	      \psfrag{to}[c][c]{\(t\)}
	      \psfrag{da}[c][c]{\parbox{3cm}{\centering \tiny continuous\\ motion data}}
	      \psfrag{w}[c][c]{\(\scriptstyle W\)}
	      \psfrag{slid}[c][c]{\parbox{1cm}{\centering \tiny sliding \\windows}}
	      \psfrag{c}[c][c]{\(\scriptstyle c\)}
	      \psfrag{0}[c][c]{\(\scriptstyle 0\)}
              \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/HMM_SlidWind05.eps}
    \end{figure}}
   \only<6->{\begin{figure}
             \psfrag{s1}[c][c]{\(s_1\)}
	      \psfrag{s2}[c][c]{\(s_2\)}
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	      \psfrag{da}[c][c]{\parbox{3cm}{\centering \tiny continuous\\ motion data}}
	      \psfrag{w}[c][c]{\(\scriptstyle W\)}
	      \psfrag{slid}[c][c]{\parbox{1cm}{\centering \tiny sliding \\windows}}
	      \psfrag{c}[c][c]{\(\scriptstyle c\)}
	      \psfrag{0}[c][c]{\(\scriptstyle 0\)}
              \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/HMM_SlidWind3.eps}
    \end{figure}}

    \only<3>{\begin{figure}
             \psfrag{s1}[c][c]{\(s_1\)}
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	      \psfrag{c}[c][c]{\(\scriptstyle c\)}
	      \psfrag{0}[c][c]{\(\scriptstyle 0\)}
              \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/HMM_SlidWind05.eps}
    \end{figure}}

     \only<1-2>{\begin{figure}
             \psfrag{s1}[c][c]{\(s_1\)}
	      \psfrag{s2}[c][c]{\(s_2\)}
	      \psfrag{sT}[c][c]{\(s_T\)}
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	      \psfrag{da}[c][c]{\parbox{3cm}{\centering \tiny continuous\\ motion data}}
	      \psfrag{w}[c][c]{\(\scriptstyle W\)}
	      \psfrag{slid}[c][c]{}
	      \psfrag{c}[c][c]{\(\scriptstyle c\)}
	      \psfrag{0}[c][c]{\(\scriptstyle 0\)}
              \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/HMM_SlidWind0.eps}
    \end{figure}}


\uncover<2->{\begin{tabular}{p{0.48\textwidth}p{0.48\textwidth}}
    HMM Concept:  &                                                                 \only<5->{Segmentation Procedure }\\ 
    \vspace{-4mm} \begin{itemize}
    \item<3-> \footnotesize Each sliding window (length \(W\)) \\ \(\widehat{=}\) HMM state 
    \item<4-> \footnotesize Relevant parameters:\begin{flushleft}
                                                 \begin{tabular}{rl}
                                                 -& Transition cost \(c\) \\
						 -& Standard deviation \(\sigma\)
                                                \end{tabular}
						\end{flushleft}

 
    \end{itemize} &
     \vspace{-5mm} \begin{enumerate}
                   \item<6-> \footnotesize If new state created, \(s\in\mathcal{S}=\left\{1,\dots,T\right\}\)
		    \item<7-> \footnotesize Find optimum state at time \(T\) (\emph{Viterbi} \cite{tutorialHMM})
		    \item<8-> \footnotesize Switch to new segment, if optimum state changed 
                  \end{enumerate}
\end{tabular}}
   \only<5->{ \begin{pspicture}(0,0)
      \qline(0.2,0.6)(0.2,4.3)
    \end{pspicture}}

\end{frame}     


\section{Parameter Estimation}

\begin{frame}
   \frametitle{Semi-supervised Parameter Estimation}
    ISSUE: Several parameters for HMM Definition required
    \begin{block}{Challenge}
       automatic adjustment to incoming data desired\\
      \(\rightarrow\) Semi-supervised parameter estimation for \begin{itemize}
                                                                \item the limits of \(\sigma\)
								\item \only<1>{the transition cost}\only<2->{\textbf{the transition cost}}
                                                               \end{itemize}

   \end{block}
\end{frame}

% \begin{frame}
%     \frametitle{Important HMM Parameters}
% \begin{pspicture}(1.0\textwidth,-5)(0,3)% \psgrid
% % Distance Marker
% \only<6>{\psframe[linecolor=black,
% 				fillcolor=back,
% 				fillstyle=solid]
% 				(6.65,0.42)(7.37,0.95)
% \pscurve{->}(3.05,0.6)(5,1)(6.65,0.85)}
% 
% 
% % Cost previous Marker
% \only<7>{\psframe[linecolor=black,
% 				fillcolor=back,
% 				fillstyle=solid]
% 				(8.28,0.42)(9.65,0.95)
% \pscurve{->}(7,-0.32)(8.2,0.0)(8.48,0.32)
% \rput[mt](7,-0.4){\parbox{3cm}{\footnotesize\centering cost of state \(s\)\\ at previous timestep}}
% }
% % Transition Marker
% \only<8>{\psframe[linecolor=black,
% 				fillcolor=back,
% 				fillstyle=solid]
% 				(9.74,0.42)(11.67,0.95)
% 
% \pscurve{->}(10,-0.32)(10.4,0)(10.6,0.32)
% \rput[mt](10,-0.4){\parbox{3cm}{\footnotesize\centering cost of other state\\ at previous timestep \(+\) transition cost \(c\) to state \(s\)}}
% }
% 
% \only<4->{\qline(5.5,0)(5.5,2.4)}
% 
% \rput[lt](-0.4,2.5){\begin{tabular}{p{0.5\textwidth}p{0.5\textwidth}}
%  \parbox{0.5\textwidth}{\small \centering Standard deviation \(\sigma\)} &  \only<4->{\parbox{0.5\textwidth}{\centering \small Transition cost \(c\)}}  \\
% \hspace{-2mm} \vspace{-2mm}\begin{itemize}
%                             \item<2->  \footnotesize \(\sigma\widehat{=}\) Averaged standard deviation of time series
%                             \item<3-> \footnotesize Distance \(d_{s,t}\sim\frac{1}{\sigma}\)\\
% 			    \(\rightarrow\) \(\sigma\) serves as sensibility control
%                            \end{itemize}
% 		          & \vspace{-2mm}\begin{itemize}
%                             \item<5-> \footnotesize  Cost updates:
% 				\vspace{-3mm}\begin{align*}c_s(T)=\qquad\qquad\qquad\qquad\qquad\\=d_{s,T}+\text{min}[c_s(T-1),o(T-1)+c]\end{align*}
% 
%                          \end{itemize} \vspace{-5mm} 
% \end{tabular}
% }
% \only<9->{\rput[tl](6,0.3){\parbox{0.9\textwidth}{\footnotesize\(\rightarrow c\) is important during cost calculation }}}
% \only<10->{
% \rput[mt](6,-0.4){\parbox{0.8\textwidth}{\flushleft\small Focusing on informational content of the time series is possible by\begin{itemize}
%                                                                                                          \item<11-> \footnotesize limiting \(\sigma\):\\ \vspace{-3mm}\begin{center} \(\sigma_{min}\stackrel{!}{\leq}\sigma\stackrel{!}{\leq}\sigma_{max}\)\end{center}
%                                                                                                          \item<12-> \footnotesize choosing the transition cost \(c\) appropriately 
% 												  \end{itemize}\only<13->{using a semi-supervised parameter estimation approach}}}
% \rput[c](2,-0.47){\rotatebox{315}{\scalebox{2}{\ding{239}}}}
% \rput[c](9,-0.4){\rotatebox{225}{\scalebox{2}{\ding{239}}}}
% }
% \end{pspicture}
% \end{frame}




% \begin{frame}
%           \frametitle{Estimating the limits of \(\sigma\)}
% \begin{pspicture}(1.0\textwidth,-5)(0,3)  %\psgrid
% \rput[lt](0,3){
% 	\psfrag{x}[lB][c]{\(\bm{x}\)}
%     \psfrag{t}[c][c]{\(t\)}
%     \psfrag{a}[b][b][0.8]{\tiny \( \stackrel{\longleftrightarrow}{W}\)}
%     \psfrag{Da}{\footnotesize Data:}
%     \psfrag{Se}{\parbox{4cm}{\footnotesize Segment points:}}
%     \psfrag{bl}{\footnotesize Estimation Result:}
%     \psfrag{pl}{\(+\)}
%     \psfrag{eq}[cb][c][1][90]{\tiny\(\Longleftarrow\)}
%     \psfrag{sig}[c][c][0.95]{\small\(\underbrace{}_{\displaystyle \tilde{\sigma}}\)}
%     \psfrag{e1}{\footnotesize\textit{If} \(\tilde{\sigma}>\sigma_{max} \rightarrow \sigma_{max}=\tilde{\sigma}\)}
%     \psfrag{e2}{\footnotesize\textit{Else If} \(\tilde{\sigma}<\sigma_{min} \rightarrow \sigma_{min}=\tilde{\sigma}\)}   
%     \psfrag{ts}[c][c]{}%\footnotesize\(t_{seg}\)}
% 	\includegraphics[width=1\textwidth]{./Bilder/Bilder/sigmaestimation.eps}}
% \only<1>{\psframe[linecolor=white,
% 				fillcolor=white,
% 				fillstyle=solid]
% 				(0,-2.18)(7,-3.5)}
% \only<3->{\rput[lt](2,-3.5){\parbox{0.7\textwidth}{\(\Rightarrow\) Focusing on informational content of data}}}
% \end{pspicture}
% \end{frame}


\begin{frame}
   \frametitle{E.g.: Semi-supervised Transition Cost Estimation}
\begin{pspicture}(1.0\textwidth,-5)(0,3)  %\psgrid
\only<1>{\rput[lt](0,3){
    \psfrag{Da}{\tiny Time series:}
    \psfrag{Se}[lt][t]{\parbox{4cm}{\tiny Segment points}}
    \psfrag{x}[lB][c]{\tiny\(\bm{x}\)}
    \psfrag{t}[c][cb]{\tiny\(t\)}
    \psfrag{c}[cb][cb]{\parbox{2cm}{\centering\tiny state\\ change}}
    \psfrag{n}[cb][cB]{\parbox{2cm}{\centering\tiny no state\\ change}}
    \includegraphics[width=1\textwidth,height=0.35\textwidth]{./Bilder/Bilder/transest0.eps}}}

\only<2->{\rput[lt](-0,3){
    \psfrag{Da}{\tiny Time series}
    \psfrag{Se}[lt][t]{\parbox{4cm}{\tiny Segment points}}
    \psfrag{x}[lB][c]{\tiny\(\bm{x}\)}
    \psfrag{t}[c][cb]{\tiny\(t\)}
    \psfrag{c}[cb][cb]{\parbox{2cm}{\centering\tiny state\\ change}}
    \psfrag{n}[cb][cB]{\parbox{2cm}{\centering\tiny no state\\ change}}
    \includegraphics[width=1\textwidth,height=0.35\textwidth]{./Bilder/Bilder/transest1.eps}}}

\only<2->{\rput[lt](0,-0.8){\parbox{\textwidth}{\footnotesize \textbf{Assumptions}:\\\vspace{-5mm}   \begin{itemize}
     \item<2-> \footnotesize No state change, as long as no segment point occurs 
      \item<3-> \footnotesize A newly created state \(T\) was \emph{not} part of transitions at times \(t<T\)
   \end{itemize}}}}
\only<4->{\rput[lt](-0.07,-2.4){ \parbox{\textwidth}{ \footnotesize\textbf{Result}:
   \vspace{-2mm}\begin{center} 
	   \footnotesize \(c_{seg}<c<c_{noseg}\)
   \end{center}

\vspace{-2mm} \footnotesize\only<5->{\centering\normalsize\(\Rightarrow\) An estimation of \(c\) can be derived from the above range}}}}
\end{pspicture}
\end{frame}

\begin{frame}
\frametitle{Experiment}
\begin{pspicture}(1.0\textwidth,-5)(0,3)  %\psgrid
 
 \rput[tl](-0.5,2.5){\parbox{0.45\textwidth}{
 \psfrag{joystick}[c][c]{\fcolorbox{black}{white}{\parbox{0.7cm}{\tiny joystick}}}
     \psfrag{scr}{\fcolorbox{black}{white}{\parbox{1cm}{\tiny screen for observing performed motions}}}
\includegraphics[width=0.45\textwidth]{./Bilder/Bilder/HapticDevice.eps} \\ \footnotesize \textcolor{blue}{Figure:} Haptic Device for performing 2D motions}
}
 \rput[tl](0.5\textwidth,1.45){\parbox{0.5\textwidth}{\parbox{0.25\textwidth}{
 \psfrag{1}[c][c]{\tiny1}
     \psfrag{2}{\tiny2}
     \psfrag{3}{\tiny3}
    \psfrag{4}{\tiny4}
     \psfrag{5}{\tiny5}
     \includegraphics[width=0.25\textwidth]{./Bilder/Bilder/Flower.eps}
}\parbox{0.25\textwidth}{
\psfrag{1}{\tiny1}
    \psfrag{2}{\tiny2}
    \psfrag{3}{\tiny3}
    \psfrag{4}{\tiny4}
    \psfrag{5}{\tiny5}
    \psfrag{6}{\tiny6}
    \psfrag{7}{\tiny7}
    \includegraphics[width=0.25\textwidth]{./Bilder/Bilder/House.eps} 
}
\footnotesize \textcolor{blue}{Figure:} Geometric shapes performed with the haptic Device. The numbers indicate the sequence of movement
}}

\rput[tl](0,-3){\parbox{\textwidth}{\(\Rightarrow\) Segmentation of the geometric shapes into its primitives/partial actions desired}}
\end{pspicture}

\end{frame}

\begin{frame}
 \frametitle{Application of the Algorithm} 
\begin{pspicture}(1.0\textwidth,-5)(0,3)  %\psgrid
\only<4->{\rput[tl](-0.5,-0.2){\parbox{1.4\textwidth}{\parbox{0.7\textwidth}{
  \psfrag{100}[r][r]{\tiny 100}
      \psfrag{90}[r][r]{}
      \psfrag{80}[r][r]{\tiny 80}
      \psfrag{70}[r][r]{}
      \psfrag{60}[r][r]{\tiny 60}
      \psfrag{50}[r][r]{}
      \psfrag{40}[r][r]{\tiny 40}
      \psfrag{30}[r][r]{}
      \psfrag{20}[r][r]{\tiny 20}
      \psfrag{10}[r][r]{}
      \psfrag{0}[r][r]{\tiny 0}
      \psfrag{recognized}[l][l][0.5]{ \small recognised}
      \psfrag{subsegmented}[l][l][0.5]{ \small subsegmented}
      \psfrag{not recognized}[l][l][0.5]{ \small not recognized}
      \psfrag{per}[c][c][1]{\tiny Percentage [\%]}
      \psfrag{1}[t][t]{\tiny  a.1}
      \psfrag{2}[t][t]{\tiny  a.2}
      \psfrag{3}[t][t]{\tiny  a.3}
      \psfrag{4}[t][t]{\tiny  a.4}
      \psfrag{5}[t][t]{\tiny  a.5}
    \includegraphics[width=0.7\textwidth,height=3cm]{./Bilder/Bilder/results_flower.eps}}\quad\parbox{0.3\textwidth}{\footnotesize \textcolor{blue}{Figure:} Results for each primitive after applying the segmentation
    algorithm with the parameter estimation to the time series data\\ \tiny (only for the flower shape)}
}}}

\only<1>{\rput[tl](-0.5,3){\parbox{1.4\textwidth}{\parbox{0.7\textwidth}{
    \psfrag{x}{\tiny\(\bm{x}\)}
    \psfrag{t}{\tiny\(t\)}
    \psfrag{s}[c][c][0.8]{\footnotesize segment}
    \psfrag{r}[c][c][0.8]{}
    \includegraphics[width=0.7\textwidth,height=3cm]{./Bilder/Bilder/Results_Filtered2_rec.eps}}\quad\parbox{0.3\textwidth}{\footnotesize \textcolor{blue}{Figure:} Example of segmented data}}}}

\only<2>{\rput[tl](-0.5,3){\parbox{1.4\textwidth}{\parbox{0.7\textwidth}{
    \psfrag{x}{\tiny\(\bm{x}\)}
    \psfrag{t}{\tiny\(t\)}
    \psfrag{s}[c][c][0.8]{not recognized}
    \psfrag{r}[c][c][0.8]{}
    \includegraphics[width=0.7\textwidth,height=3cm]{./Bilder/Bilder/Results_Filtered2_no.eps}}\quad\parbox{0.3\textwidth}{\footnotesize \textcolor{blue}{Figure:} Example of segmented data
}}}}


\only<3->{\rput[tl](-0.5,3){\parbox{1.4\textwidth}{\parbox{0.7\textwidth}{
    \psfrag{x}{\tiny\(\bm{x}\)}
    \psfrag{t}{\tiny\(t\)}
    \psfrag{s}[c][c][0.8]{\footnotesize segment}
    \psfrag{r}[c][c][0.8]{\footnotesize  subsegment}
    \includegraphics[width=0.7\textwidth,height=3cm]{./Bilder/Bilder/Results_Filtered2.eps}}\quad\parbox{0.3\textwidth}{\footnotesize \textcolor{blue}{Figure:} Example of segmented data
}}}}
\only<5->{\rput[mt](5.5,-3.5){\parbox{\textwidth}{\centering \(\Rightarrow\) Compromise between subsegmenting and amount of recognized segments cannot be avoided}}}


\end{pspicture}
\end{frame}

\section{Clustering Subsegments}

 \begin{frame}
   \only<2->{\frametitle{Clustering Subsegments}}
   \only<1>{\frametitle{Primitive base Learning}}
 	% State of the Art	   
             \begin{pspicture}(1.0\textwidth,-5)(0,3) % \psgrid
	  \only<1>{ 
		
 	       \rput[lt](1,2.5){ 	 
	  \psfrag{da}[c][c]{\parbox{3cm}{\tiny \centering continuous haptic and \\motion time series}}
          \psfrag{se}[c][c]{\parbox{3cm}{\tiny \centering online segmentation}}
 	  \psfrag{en}[c][ct]{\tiny HMM encoding}
 	  \psfrag{tr}[c][c]{\parbox{3cm}{\tiny \centering primitive \\knowledge base}}
 	  \psfrag{desc}[t][c][1.1]{\parbox{5cm}{\footnotesize Unavoidability of \emph{subsegmenting}}}
 	 \includegraphics[width=0.8\textwidth]{./Bilder/Bilder/clustering_base.eps}
	  
        }
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\begin{frame}
    \frametitle{An Approach for Clustering Subsegments}
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      \end{pspicture}

\end{frame}


\begin{frame}
      \frametitle{Application of the Subclustering Approach}
 \begin{pspicture}(1.0\textwidth,-5)(0,3) %\psgrid


\rput[tm](5.5,2.2){\parbox{\textwidth}{\textbf{Experiment:}
       \begin{enumerate}
       \item<1-> \footnotesize Training of several clusters with segments gained during segmentation
        \item<2-> \footnotesize Exemplary testing of the approach with subsegments occuring during segmentation
       \end{enumerate}}}
 
 
 \only<3->{\rput[tm](5.5,0){\parbox{\textwidth}{\textbf{Results:}
       \begin{itemize}
       \item<4->  \footnotesize A \emph{filtering of subsegments} not improving the learned behavior was possible by correctly adjusting the certainty threshold
        \item<5-> \footnotesize After the subclustering:\\\hspace{-0.3cm}\scriptsize\begin{minipage}[t]{0.5\textwidth} $ \left. \begin{array}{rl}&\text{In 93\% of the cases the \emph{likelihood}}\\ 
 							   &\text{In 85\% of the cases the \emph{certainty}}\end{array} \right\} \mbox{\parbox{5cm}{\centering between subsegment and newly trained HMM increased}}$ \end{minipage}
       \end{itemize}
 }}}

\only<6->{ \rput[tm](5.5,-2.6){\parbox{\textwidth}{\(\rightarrow\) \footnotesize Clustering of subsegments is possible}}}

  
\only<6->{\rput[tm](5.5,-3.6){\parbox{\textwidth}{\centering   \normalsize  \(\Rightarrow\)Wrongly trained clusters can be avoided}}}
  	  
\end{pspicture}

\end{frame}

\section{Conclusion}

\begin{frame}
	\frametitle{Conclusion}
 \begin{pspicture}(1.0\textwidth,-5)(0,3) %\psgrid

\rput[tm](5.5,2.2){\parbox{\textwidth}{\textbf{Semi-supervised segmentation:}
 \begin{itemize}
  \item<1-> \footnotesize Meaningful parameter estimations are gainable
  \item<2-> \footnotesize\(\sim\) 75\% of correctly recognized segments
 \end{itemize}
 \only<3->{\footnotesize\emph{BUT:} Subsegmenting not completely avoidable}
}}
 
\only<4->{\rput[tm](5.5,0){\parbox{\textwidth}{ \centering \scalebox{2}{\(\Downarrow\)}}}}


\only<4->{\rput[tm](5.5,-1){\parbox{\textwidth}{\textbf{Clustering subsegments:}
 \begin{itemize}
  \item<5-> \footnotesize Presented approach allows integration of subsegments into clusters
  \item<6-> \footnotesize Certainty specifies how likely an improvement of learned behavior would be
  \item<7-> \footnotesize Extension of an incremental learning framework with this feature might be reasonable
 \end{itemize}
}}}
\end{pspicture}

\end{frame}



% \begin{frame}
%   \frametitle{Motivation for a Clustering of Subsegments}
%   \begin{pspicture}(1.0\textwidth,-5)(0,3) % \psgrid
%     \rput[lt](0.4,1.5){\parbox{\textwidth}{\textbf{\footnotesize Usually applied clustering concept:} \begin{enumerate}
%                                                                                          \item \footnotesize encoding of new segment observation \(O\) into HMM \(\lambda_O\)
% 											 \item \footnotesize computation of symmetric Kullback-Leibler divergence \cite{ScaffSeg} of \(\lambda_O\) with each HMM in a cluster
% 											 \item \footnotesize If one distance is below a threshold add \(O\) to corresponding cluster 
%                                                                                         \end{enumerate}
% 
% \footnotesize\vspace{0.5cm}\begin{tabular}{rcp{0.7\textwidth}} \emph{BUT:} &-& Subsegments result in high distance values\\ &-& How to use them for improving learned behavior?\end{tabular}
% 
% }}
% 
% 
% \end{pspicture}
% \end{frame}




% \begin{frame}
%     \frametitle{An Approach for Clustering Subsegments}
%     \begin{pspicture}(1.0\textwidth,-5)(0,3) % \psgrid
%     \rput[lt](0.4,2.5){\parbox{\textwidth}{\textbf{\footnotesize Steps for clustering a subsegment:} \begin{enumerate}
% 													\item \footnotesize Finding the HMM \(\lambda_m\) within all clusters for which it is most likely to represent the newly observed subsegment
% 													\item \footnotesize Getting the overlapping position of the new observation within the generated behavior of \(\lambda_m\)
% 													\item \footnotesize Calculating how certain it is that the subsegment is represented by \(\lambda_m\)
% 													\item \footnotesize If the certainty is above a threshold, merge subsegment and \(\lambda_m\)
% 												    \end{enumerate}
%     
%     }}
%     \end{pspicture}
% \end{frame}








% \begin{frame}
%     \frametitle{Results}
%    \begin{figure}
% \centering
%     \subfigure[low leaf]{
%       
%       \psfrag{0}[r][c][0.8]{\tiny 0}
%       \psfrag{0.25}[r][c][0.8]{}
%       \psfrag{0.5}[r][c][0.8]{\tiny 0.5}
%       \psfrag{0.75}[r][c][0.8]{\tiny 0.75}
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%       \psfrag{2_}[t][c][0.8]{\tiny 1}
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%       \psfrag{step}[ct][bc][0.9]{\tiny clustering times}
%       \psfrag{cert}[c][cr][0.9]{\tiny certainty}
%       \includegraphics[width=0.2\textwidth]{./Bilder/Bilder/cert_lowLeaf.eps}
%     } 
%     \subfigure[upper leaf]{
%       
%       \psfrag{0}[r][c][0.8]{\tiny 0}
%       \psfrag{0.25}[r][c][0.8]{}
%       \psfrag{0.5}[r][c][0.8]{\tiny 0.5}
%       \psfrag{0.75}[r][c][0.8]{\tiny 0.75}
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%       \psfrag{cert}[cr][c][0.9]{\tiny certainty}
%       \includegraphics[width=0.2\textwidth]{./Bilder/Bilder/cert_upperLeaf.eps}
%     } \\
%     \subfigure[action 1to2]{
%       
%       \psfrag{0}[r][c][0.8]{\tiny 0}
%       \psfrag{0.25}[r][c][0.8]{}
%       \psfrag{0.5}[r][c][0.8]{\tiny 0.5}
%       \psfrag{0.75}[r][c][0.8]{\tiny 0.75}
%       \psfrag{1}[r][c][0.8]{\tiny 1}
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%       \psfrag{2_}[t][c][0.8]{\tiny 1}
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%       \psfrag{cert}[cr][c][0.9]{\tiny certainty}
%       \includegraphics[width=0.2\textwidth]{./Bilder/Bilder/cert_h1to2.eps}
%     } 
%     \subfigure[action 2to3]{
%       
%       \psfrag{0}[r][c][0.8]{\tiny 0}
%       \psfrag{0.25}[r][c][0.8]{}
%       \psfrag{0.5}[r][c][0.8]{\tiny 0.5}
%       \psfrag{0.75}[r][c][0.8]{\tiny 0.75}
%       \psfrag{1}[r][c][0.8]{\tiny 1}
%       \psfrag{1_}[t][c][0.8]{\tiny 0}
%       \psfrag{2_}[t][c][0.8]{\tiny 1}
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%       \psfrag{step}[ct][bc][0.9]{\tiny clustering times}
%       \psfrag{cert}[c][cr][0.9]{\tiny certainty}
%       \includegraphics[width=0.2\textwidth]{./Bilder/Bilder/cert_h2to3.eps}
%     }
%     \caption[Certainty trajectories]{Certainties for subsegments of a partial action, when applying the subclustering multiple times and keeping all newly generated HMMs.}
% \end{figure}



%\end{frame}





 

 
% \begin{frame}
%    \frametitle{An HMM Based Segmentation Approach\cite{DynHMM}}
% 
%     % Sliding Window
%    \only<1>{ \begin{figure}
% 	\begin{pspicture}(1.0\textwidth,0.5\textwidth) %\psgrid
% 	      \rput[lt](5.5,5){\parbox{6cm}{\begin{itemize}
% 	                              \item \footnotesize each sliding window (length \(W\)) \\ \(\widehat{=}\) HMM state
%                                      \end{itemize}}}
% 
% 	      \put(-0.8,-1.2){
% 	      \psfrag{vd}[c][c]{\(\vdots\)}
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% 	      \psfrag{w}[c][c]{\(\scriptstyle W\)}
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%              \includegraphics[width=0.65\textwidth]{./Bilder/Bilder/HMM_Changed_withoutTrans.eps}}
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%    \end{figure}
%       }
%     %Distance
%     \only<2>{ \begin{figure}
%  	\begin{pspicture}(1.0\textwidth,0.5\textwidth) %\psgrid
%  	      \rput[lt](5.5,5){\parbox{6cm}{\begin{itemize}
%  	                              \item \footnotesize each sliding window (length \(W\)) \\ \(\widehat{=}\) HMM state \pause
%  				      \item distance \(d_{i,j}\) \\ \(\widehat{=}\) similarity of windows \(i\) and \(j\) 
%  				      \end{itemize}}}
%  
%  	      \put(-0.8,-1.2){
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%               \includegraphics[width=0.65\textwidth]{./Bilder/Bilder/HMM_Changed_withoutTrans.eps}}
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%      }
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%  	\begin{pspicture}(1.0\textwidth,0.5\textwidth) %\psgrid
%  	      \rput[lt](5.5,5){\parbox{6cm}{\begin{itemize}
%  	                              \item \footnotesize each sliding window (length \(W\)) \\ \(\widehat{=}\) HMM state
%  				      \item distance \(d_{i,j}\) \\ \(\widehat{=}\) similarity of windows \(i\) and \(j\) 
%  				      \item costs \(c_s(t)\) for being in a state \(s\) while observing a window \(t\)
%  	                             \end{itemize}}}
%  
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%             \includegraphics[width=0.65\textwidth]{./Bilder/Bilder/HMM_Changed_withoutTrans.eps}}
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%     }
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%  	\begin{pspicture}(1.0\textwidth,0.5\textwidth) %\psgrid
%  	      \rput[lt](5.5,5){\parbox{6cm}{\begin{itemize}
%  	                              \item \footnotesize each sliding window (length \(W\)) \\ \(\widehat{=}\) HMM state
%  				      \item distance \(d_{i,j}\) \\ \(\widehat{=}\) similarity of windows \(i\) and \(j\) 
%  				      \item costs \(c_s(t)\) for being in a state \(s\) while observing a window \(t\)
%  				      \item - optimum cost buffer: \(o(t)\) \\
% 					    - transition cost \(c\)
%  	                             \end{itemize}}}
%  
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%             \includegraphics[width=0.65\textwidth]{./Bilder/Bilder/HMM_Changed_withoutTrans.eps}}
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%     }
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%  	\begin{pspicture}(1.0\textwidth,0.5\textwidth) %\psgrid
%  	      \rput[lt](5.5,5){\parbox{6cm}{\begin{itemize}
%  	                              \item \footnotesize each sliding window (length \(W\)) \\ \(\widehat{=}\) HMM state
%  				      \item distance \(d_{i,j}\) \\ \(\widehat{=}\) similarity of windows \(i\) and \(j\) 
%  				      \item costs \(c_s(t)\) for being in a state \(s\) while observing a window \(t\)
%  				      \item - optimum cost buffer: \(o(t)\)\\
% 					    - transition cost \(c\)
%  				      \item cost update:
%  					    \(c_s(T)=d_{s,T}+\text{min}[c_s(T-1),o(T-1)+c]\)
%  	                             \end{itemize}}}
%  
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%     }
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%  	\begin{pspicture}(1.0\textwidth,0.5\textwidth) %\psgrid
%  	      \rput[lt](5.5,5){\parbox{6cm}{\begin{itemize}
%  	                              \item \footnotesize each sliding window (length \(W\)) \\ \(\widehat{=}\) HMM state
%  				      \item distance \(d_{i,j}\) \\ \(\widehat{=}\) similarity of windows \(i\) and \(j\) 
%  				      \item costs \(c_s(t)\) for being in a state \(s\) while observing a window \(t\)
%  				      \item optimum cost buffer: \(o(t)\)
%  				      \item cost update:
%  					    \(c_s(T)=d_{s,T}+\text{min}[c_s(T-1),o(T-1)+c]\)
%  	                             \end{itemize}}}
%  
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%             \includegraphics[width=0.65\textwidth]{./Bilder/Bilder/HMM_Changed.eps}}
% 	\end{pspicture}
%   \end{figure}
%     }
% \end{frame}

%\begin{frame}
%    \frametitle{Statistical Approach with a HMM}
%    \textbf{Finding the most likely state sequence by}
%     \begin{enumerate}
 %     \item<1-> updating all previous costs and optimum paths: \(\forall t<T\) do
%      \begin{align*}
%       c_T(t)&=d(p_T,p_t)+\text{min}\left[ c_T(t-1),\;o(t-1)+c\right] \\
 %         o(t)&=c_T(t),\: \text{if} \; c_T(t)<o(t)
%      \end{align*}
 %     \item<2-> getting the costs \(c_s(T)\): \(\forall s\in\mathcal{S}\) do
%       \begin{equation*}
 %       c_s(T)=d(p_s,p_T)+\text{min}\left[ c_s(T-1),\;o(T-1)+c\right]
 %      \end{equation*}
%       \item<3-> finding optimum cost at time \(T\): 
%        \begin{equation*}
 %              o(T)=\text{min}_{s\in\mathcal{S}}\left[c_s(T)\right]
 %       \end{equation*}
%     \end{enumerate}
%  \uncover<4->{   with \(c=\zeta^2\log k\) being the transition cost \\
%\begin{equation*}
 %   o(T)\neq o(T-1) \qquad \Rightarrow \qquad \text{create segment}
%\end{equation*}}
%\end{frame}

%\section{Supervised Adaptation}

%\begin{frame}
%    \frametitle{Supervised Adaptation of the Algorithms Parameters}
%   \begin{block}{Which parameters are adjusted automatically?}
%       \begin{itemize}
%       \item<1-> limits for the standard deviation \(\sigma\)
%        \item<2-> transition cost \(c=\zeta^2\log k\) \\
%              \(\rightarrow\) simplifies calculation
 %      \end{itemize}
 %    \end{block}
%\end{frame}

%\begin{frame}
%    \frametitle{Supervised Adaptation of the Algorithms Parameters}
%   \begin{block}{Which parameters are adjusted automatically?}
 %      \begin{itemize}
 %      \item limits for the standard deviation \(\sigma\)
 %       \item transition cost \(c=\zeta^2\log k\) \\
 %             \(\rightarrow\) simplifies calculation
%       \end{itemize}
 %    \end{block}
 %    \begin{block}{The basic concept}
 %      \begin{itemize}
 %       \item segments are defined manually
 %       \item algorithm first calulates \(\sigma_{min}\) and \(\sigma_{max}\)
 %       \item computation of lower and upper borders for \(c\)
 %      \end{itemize}
 %   \end{block}
%\end{frame}


%\begin{frame}
 %   \frametitle{Parameter \(\sigma\)}

 %  \vspace{0.5cm}
 %  \begin{minipage}[t]{0.4\textwidth}
 %  \textbf{Parameter \(\sigma\) is:}
 %  \begin{itemize}
 %   \item included in the distance
 %   \begin{equation*}
 %       d(p_t,p_{\overline{t}})=\int (p_t-p_{\overline{t}})^2
 %   \end{equation*}
  %  \vspace{0.2cm}
 %     \item enables to adapt to fluctuations 
 %     of data 
 %  \end{itemize}   
 %   \end{minipage}
 % \begin{minipage}[t]{0.5\textwidth}
%     \textbf{Adaptation:}
 %   \begin{itemize}
 %     \item at wanted segment points \(t=t_{seg}\), compute:
 %    \begin{equation*}        
%           \sigma_{t}=\sqrt{\sum_{i=0}^{W}\frac{(\overline{\mathbf{x}}_{t}-\mathbf{x}_{t}-i)^2}{W}}
%     \end{equation*}
%     \item set \(\sigma_{min/max}\)
%    \end{itemize}
%  \end{minipage}
%\end{frame}


%\begin{frame}
%   \frametitle{Transition Cost}
%  \uncover<1->{ \textbf{assumptions:}
%   \begin{itemize}
%     \item no state change, as long as no segment occurs
%        \(\rightarrow \qquad o(T - 1) = c_s(T-1)\qquad\)  (\(s\): last state change)
%     \item new state is not part of previous state transitions
%   \end{itemize}}
%  \uncover<2->{ \textbf{result:}
 % \begin{align*}
 %     d_{s,T}&\stackrel{!}{<}c &\qquad\qquad&\rightarrow \text{no state change}&\rightarrow\text{segment} \\
 %     d_{s,T}&\stackrel{!}{>}c &\qquad\qquad&\rightarrow \text{no state change}&\rightarrow\text{segment} \\
 %  \end{align*}
 %  \(\Rightarrow\) limits for transition cost can be calculated}
%\end{frame}






\appendix

\begin{frame}[shrink]
	\frametitle{References}
	\tiny
	\bibliographystyle{plain}
	\bibliography{jube88.bib}
\end{frame}


\end{document}
